where \(cos(\mathbf {a}, \mathbf {b}) = \mathbf {a}^\top \mathbf {b} / (\Vert \mathbf {a}\Vert \Vert \mathbf {b}\Vert )\) , and \(\mathbf {t}_i\)  denotes the text embeddings of class \(i\) . We apply the standard softmax cross entropy loss on the logits (see Fig. REF ). At test time, we keep the “background” category and expand the text embeddings from \(C_B\)  to \(C_B \cup C_N\)  for open-vocabulary detection. Similar designs have been used by previous works [1]}, [2]}.
